Bonferroni-type inequalities; Chebyshev-type inequalities for the distributions on [0, n]

An elementary majorant-minorant method to construct the most stringent Bonferroni-type inequalities is presented. These are essentially Chebyshev-type inequalities for discrete probability distributions on the set {0, 1,..., n}, where n is the number of concerned events, and polynomials with specific properties on the set lead to the inequalities. All the known results are proved easily by this method. Further, the inequalities in terms of all the lower moments are completely solved by the method. As examples, the most stringent new inequalities of degrees three and four are obtained. Simpler expressions of Mrgritescu's inequality (1987, Stud. Cerc. Mat., 39, 246–251), improving Galambos' inequality, are given.     

Preparation,structures, and redox and emission characteristics of the isothiocyanate complexes of hexarhenium(III) clusters [Re6(mu3-E)8(NCS)6]4- (E = S,Se)

Hexarhenium(III) complexes with terminal isothiocyanate ligands, [(n-C(4)H(9))(4)N](4)[Re(6)(mu(3)-S)(8)(NCS)(6)] (1) and (L)(4)[Re(6)(mu(3)-Se)(8)(NCS)(6)] (L(+) = PPN(+) (2a), (n-C(4)H(9))(4)N(+) (2b)), have been prepared by three different methods. Complex 1 was prepared by the reaction of [(n-C(4)H(9))(4)N](4)[Re(6)(mu(3)-S)(8)Cl(6)] with molten KSCN at 200 degrees C, while 2b was obtained by refluxing the chlorobenzene-DMF (2:1 v/v) solution of [Re(6)(mu(3)-Se)(8)(CH(3)CN)(6)](SbF(6))(2) and [(n-C(4)H(9))(4)N]SCN. The [Re(6)(mu(3)-Se)(8)(NCS)(6)](4)(-) anion was also obtained from a mixture of Cs(2)[Re(6)(mu(3)-Se)(8)Br(4)] and KSCN in C(2)H(5)OH by a mechanochemical activation at room temperature for 20 h and isolated as 2a. The X-ray structures of 1 and 2a.4DMF have been determined (1, C(70)H(144)N(10)S(14)Re(6), monoclinic, space group P2(1)/n (No. 14), a = 14.464(7) A, b = 22.059(6) A, c = 16.642(8) A, beta = 113.62(3) degrees, V = 4864(3) A(3), Z = 2; 2a.4DMF, C(162)H(144)N(14)O(4)P(8)S(6)Se(8)Re(6), triclinic, space group P1 (No. 2), a = 15.263(2) A, b = 16.429(2) A, c = 17.111(3) A, alpha = 84.07(1) degrees, beta = 84.95(1) degrees, gamma = 74.21(1) degrees, V = 4098.3(8) A(3), Z = 1). All the NCS(-) ligands in both complexes are coordinated to the metal center via nitrogen site with the Re-N distances in the range of 2.07-2.13 A. The redox potentials of the reversible Re(III)(6)/Re(III)(5)Re(IV) process in acetonitrile are +0.84 and +0.70 V vs. Ag/AgCl for [Re(6)(mu(3)-S)(8)(NCS)(6)](4)(-) and [Re(6)(mu(3)-Se)(8)(NCS)(6)](4)(-), respectively, which are the most positive among the known hexarhenium complexes with six terminal anionic ligands. The complexes show strong red luminescence with the emission maxima (lambda(max)/nm), lifetimes (tau(em)/micros), and quantum yields (phi(em)) being 745 and 715, 10.4 and 11.8, and 0.091 and 0.15 for 1 and 2b, respectively, in acetonitrile. The data reasonably well fit in the energy-gap plots of other hexarhenium(III) complexes. The temperature dependence of the emission spectra and tau(em) of 1 and [(n-C(4)H(9))(4)N](4)[Re(6)(mu(3)-S)(8)Cl(6)] are also reported.     

Synthesis and photoluminescence properties of BF2 complexes with 1,3-diketone ligands

BF₂ complexes with 1,3-diketone ligands were synthesized, and their optical and electrochemical properties were studied. The colors of the complexes varied depending on the structures of the 1,3-diketone ligands. The absorption and emission maxima of the complexes with 1,3-diaryl-1,3-diketone ligands were considerably red shifted as compared to those of the complexes with 1-aryl-3-trifluoromethyl-1,3-diketone ligands, suggesting an extended π-conjugation of the 1,3-diaryl-1,3-diketone moieties. The molar absorption coefficients and quantum yields of the complexes with 1,3-diaryl-1,3-diketone ligands were larger than those of the complexes with 1-aryl-3-trifluoromethyl-1,3-diketone ligands. Cyclic voltammetry measurements revealed that the reduction potentials of the BF₂ complexes were higher than those of the free ligands. These complexes exhibited various emission colors in the solid states due to the intermolecular interactions.     

R3Al-R'3SiOTf: novel and powerful reagent system for stereospecific alkylation-silylation reactions of epoxides

[reaction: see text] A novel and powerful reagent system R(3)Al-R'(3)SiOTf for the one-pot alkylation-silylation reaction of epoxides was discovered, and the reactions of various epoxides with the new reagent system have been demonstrated to occur stereospecifically giving rise to the corresponding alkylation-silylation products in excellent yields.     

Diinsertion of fluorenylidene into a sulfur-sulfur bond of diaryl disulfides

Upon irradiation (>340 nm) of a benzene solution of diazofluorene with di-p-tolyl- or di-p-anisyl disulfide, the corresponding 9,9′-bis(arylmercapto)bifluorenyl was afforded in moderate to good yield accompanied by formation of 9,9′-bis(arylmercapto)fluorene. The major reaction pathway is considered to be a disulfur ylide formation followed by two times of successive Stevens rearrangement or by concerted electron redistribution via [2,3]sigmatropic rearrangement.     

Effect of amount of monomer on radiation-induced polymerization of styrene adsorbed on silica gel

The effect of amount of monomer on radiation-induced polymerization of styrene adsorbed on silica gel was investigated with the monomer amounting from less than monolayer adsorption to more than the equilibrium adsorption. The rate of graft polymerization and the molecular weight of the polymer changed with the amount of monomer adsorbed on silica gel. Maximum grafting efficiency was obtained at monolayer adsorption. The molecular weight of graft polymer was higher than that of homopolymer in both radical and cationic polymerizations, and the ratio in molecular weight of graft polymer to that of homopolymer tends to be unity with increasing amount of adsorbed monomer. These results can mainly be explained in terms of the number of initiating species (radical and cation) that change in relation to the amount of adsorbed monomer. Propagation and termination change with amount of adsorbed monomer in relation to the molecular mobility of adsorbed monomer. A very high-molecular-weight graft polymer is formed only with a small amount of adsorbed monomer in the initial stage. The grafting percent with a large amount of adsorbed monomer increased after most of the monomer has been polymerized. Secondary effect of radiation on the graft and homopolymers due to energy transfer from silica gel is suggested from the complicated phenomena in the later stage of the reaction.     

Central limit theorems for realized volatility under hitting times of an irregular grid

We consider a continuous semi-martingale sampled at hitting times of an irregular grid. The goal of this work is to analyze the asymptotic behavior of the realized volatility under this rather natural observation scheme. This framework strongly differs from the well understood situations when the sampling times are deterministic or when the grid is regular. Indeed, neither Gaussian approximations nor symmetry properties can be used. In this setting, as the distance between two consecutive barriers tends to zero, we establish central limit theorems for the normalized error of the realized volatility. In particular, we show that there is no bias in the limiting process.     

SYNTHESIS AND CHARACTERIZATION OF KINETICALLY STABILIZED 1,3-DIPHOSPHACYCLOBUTENE DERIVATIVES

1-(2,4,6-Tri-tert-butylphenyl)-2-phosphaethyne (1) was allowed to react with 0.5 equiv of an alkyllithium and subsequently with an alcohol to afford a bulky 1,3-diphosphacyclobutene, and its structure and coordination properties on transition metals were investigated. On the other hand, 1 was allowed to react with an alkyllithium and iodomethane to form a stable biradical, 1,3-diphosphacyclobutane-2,4-diyl.     

On the classification of weighing matrices and self‐orthogonal codes

We provide a classification method of weighing matrices based on a classification of self‐orthogonal codes. Using this method, we classify weighing matrices of orders up to 15 and order 17, by revising some known classification. In addition, we give a revised classification of weighing matrices of weight 5. A revised classification of ternary maximal self‐orthogonal codes of lengths 18 and 19 is also presented. © 2011 Wiley Periodicals, Inc. J Combin Designs 20:40–57, 2012     

Synthesis and Self‐Assembly of Cyclic 2,7‐Anthrylene Ethynylene 1,3‐Phenylene Ethynylene Trimer with a Planar Conformation

Cyclic arylene ethynylene hexamer 1 , composed of alternating 2,7‐anthrylene ethynylene units and meta‐phenylene ethynylene units, was synthesized. It shows C₃ symmetry and possesses a flat and rigid conformation with a large equilateral triangle‐like cavity. Macrocycle 1 self‐associates through π–π stacking interactions between the anthracene‐containing macrocyclic aromatic cores with indefinite‐association constant K_E=6980 m ^?1 in CDCl₃ at 303 K. Macrocycle 1 also self‐assembles into π‐stacked nanofibers in the drop‐cast film.